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  2. Forbidden subgraph problem - Wikipedia

    en.wikipedia.org/wiki/Forbidden_subgraph_problem

    In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph , find the maximal number of edges ⁡ (,) an -vertex graph can have such that it does not have a subgraph isomorphic to .

  3. List coloring - Wikipedia

    en.wikipedia.org/wiki/List_coloring

    For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.

  4. Elementary Number Theory, Group Theory and Ramanujan Graphs

    en.wikipedia.org/wiki/Elementary_Number_Theory...

    Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...

  5. Graph sandwich problem - Wikipedia

    en.wikipedia.org/wiki/Graph_sandwich_problem

    The graph sandwich problem is NP-complete when Π is the property of being a chordal graph, comparability graph, permutation graph, chordal bipartite graph, or chain graph. [2] [4] It can be solved in polynomial time for split graphs, [2] [5] threshold graphs, [2] [5] and graphs in which every five vertices contain at most one four-vertex ...

  6. De Bruijn–Erdős theorem (graph theory) - Wikipedia

    en.wikipedia.org/wiki/De_Bruijn–Erdős_theorem...

    In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that, when all finite subgraphs can be colored with c {\displaystyle c} colors, the same is true for the whole graph.

  7. Category:Unsolved problems in graph theory - Wikipedia

    en.wikipedia.org/wiki/Category:Unsolved_problems...

    Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Unsolved problems in graph theory" The following 32 pages are in this ...

  8. Dessin d'enfant - Wikipedia

    en.wikipedia.org/wiki/Dessin_d'enfant

    The name of these embeddings is French for a "child's drawing"; its plural is either dessins d'enfant, "child's drawings", or dessins d'enfants, "children's drawings". A dessin d'enfant is a graph, with its vertices colored alternately black and white, embedded in an oriented surface that, in many cases, is simply a plane.

  9. Barnette's conjecture - Wikipedia

    en.wikipedia.org/wiki/Barnette's_conjecture

    Barnette's conjecture is an unsolved problem in graph theory, a branch of mathematics, concerning Hamiltonian cycles in graphs. It is named after David W. Barnette , a professor emeritus at the University of California, Davis ; it states that every bipartite polyhedral graph with three edges per vertex has a Hamiltonian cycle.